Electric-Field and Doping-Induced Non collinear Magnetic Interactions in Monolayer Ti$_2$Si

TL;DR

This study addresses the challenge of realizing Dzyaloshinskii–Moriya interactions (DMI) in a centrosymmetric 2D silicide, Ti$_2$Si, by combining perpendicular electric-field tuning with chemical doping. It employs density-functional theory with a Hubbard $U$ term and spin–orbit coupling, complemented by constrained-magnetization energy differences and a Wannier-based tight-binding model to quantify exchange $J$, single-ion anisotropy $K_{b_mu}$, and DMI vectors $\,\vec{d_1}\,$ and $\vec{d_2}$. Pristine Ti$_2$Si shows FM order with field-tunable $J$ and $K_{b_mu}$ but no DMI due to preserved inversion symmetry; doping with Pt and Co breaks symmetry and yields a Pt-mediated interlayer DMI, with Pt$_{0.5}$CoTi$_{0.5}$Si exhibiting the strongest chirality ($D_1=0.21$ mJ/m$^2$, $D_2=-0.50$ mJ/m$^2$). This work demonstrates a viable route to engineer and control chiral spin textures in 2D silicides, enabling voltage-tunable spintronic functionalities in atomically thin materials.

Abstract

Two-dimensional (2D) silicides are an emerging class of materials whose magnetic and relativistic properties remain largely unexplored. Using first-principles calculations, we investigate how electric-field modulation and transition-metal doping influence the magnetic exchange, magnetocrystalline anisotropy, and antisymmetric Dzyaloshinskii-Moriya interaction (DMI) in monolayer Ti2Si. Pristine Ti2Si is a dynamically stable ferromagnetic metal with in-plane anisotropy and centrosymmetric bonding, which suppresses DMI even under strong perpendicular electric fields. To overcome this symmetry constraint, we introduce Pt and Co substitution at Ti sites. Co enhances the magnetic exchange, whereas Pt provides strong spin orbit coupling (SOC), and the combined chemical asymmetry breaks inversion symmetry sufficiently to induce a sizable DMI. A Wannier-based tight-binding model captures the orbital-resolved superexchange pathways and reveals a clear hierarchy between a weak Si-mediated channel and a dominant Pt-mediated interlayer channel. First-principles calculations confirm that the Pt-assisted pathway governs the magnitude and sign of the total DMI. Among all configurations, Pt0.5CoTi0.5Si exhibits the strongest chiral interaction, with its intralayer and interlayer contributions favoring opposite rotation senses, namely counterclockwise (CCW) and clockwise (CW). Our results establish chemically engineered Ti2Si monolayers as a promising platform for realizing and tuning chiral magnetic textures in 2D silicides.

Figures (6)

• Figure 1: (a) Top and side views of the Ti$_2$Si monolayer, where $a$ denotes the lattice constant and $\theta$ represents the bond angle. (b) Phonon dispersion confirming the dynamical stability of the system. (c) Spin-polarized projected density of states (PDOS) of the Ti$_2$Si monolayer. (d) and (e) Schematic representations of the ferromagnetic and antiferromagnetic spin configurations, respectively. (f) Heisenberg exchange interaction parameter $J$ as a function of external electric field. (g) Single-ion anisotropy as a function of external electric field, where the blue region indicates out-of-plane magnetic anisotropy (OMA) and the yellow region corresponds to in-plane magnetic anisotropy (IMA).
• Figure 2: Spin-resolved density of states of the Ti$_2$Si monolayer calculated under an applied electric field of 0.4 V/Å.
• Figure 3: (a)Schematic representation of the asymmetric Ti/Pt–Si–Ti/Co exchange pathway in the doped Ti$_2$Si monolayer. Pt provides strong SOC on one side and Co strengthens the exchange interaction on the other, together creating the conditions required for a finite DMI. (b) Relaxed atomic structure of the Pt$_{0.5}$CoTi$_{0.5}$Si configuration, illustrating the asymmetric coordination created by simultaneous Pt and Co substitution. (c) Orbital-projected band structure of Pt$_{0.5}$CoTi$_{0.5}$Si strcuture.
• Figure 4: Evolution of the (a) exchange interaction $J$ and (b) magnetic anisotropy $K_{\mu}$ across different doped Ti$_2$Si configurations. The abbreviations correspond to: A$_1$ = Pt$_{0.5}$Ti$_{1.5}$Si, A$_2$ = Pt$_{0.5}$Co$_{0.5}$Ti$_{1}$Si, A$_3$ = Pt$_{0.5}$Co$_{1}$Ti$_{0.5}$Si, A$_4$ = CoTiSi, and A$_5$ = PtTiSi.
• Figure 5: (a) Schematic representation of a TM silicide, where M$_1$ and M$_2$ are magnetic transition-metal sites and X is a nonmagnetic ligand. (b) The minimal trimer model consisting of two magnetic sites, M$_1$ and M$_2$, each hosting a $d$ orbital, bridged by a nonmagnetic ligand X carrying either a $p$ or $d$ orbital. The magnetic moments on M$_1$ and M$_2$ are canted by an angle $\phi$ with respect to the $x$-axis.